2008/07/18 by Wing Kai Ho, Ho, Wing Kai · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Computational Geometry and Mesh Generation #Graph Labeling and Dimension Problems #math.DG #msc:52C22
paper · pdf · doi:10.48550/arxiv.0807.2934
This is a very preliminary version of a paper about blocking numbers of compact Riemannian surfaces, the aim is to show that if the blocking number is finite, then the surface has to be flat. edit: similar results for 2-dimensional torus have been obtained by V. Bangert and E. Gutkin, reference to their paper has been added v3: minor changes with the references
The blocking number of a manifold is the minimal number of points needed to block out lights between any two given points in the manifold. It has been conjectured that if the blocking number of a manifold is finite, then the manifold must be flat. In this paper we prove that this is true for 2-dimensional manifolds with non-trivial fundamental groups.